Learn Polish: Mimo lawiny osiągnęliśmy szczyt góry. - Despite the avalanche, we reached the summit of the mountain.

The word mimo (despite) requires the noun following it to be in the Genitive case. Since lawina is a feminine noun ending in -a, its Genitive form ends in -y, making it lawiny.

Is there a difference between starting this sentence with mimo versus pomimo?

No, you can use them completely interchangeably here! Both mimo lawiny and pomimo lawiny mean exactly the same thing and both require the noun to take the Genitive case.

The dictionary form of the verb is osiągnąć (to reach). Why does it change to ę in osiągnęliśmy?

Verbs ending in -ąć change their ą to ę in most past tense forms. Because osiągnęliśmy is the "we" form for a group with at least one male, the vowel changes to ę. If it were a group of only women speaking, it would be osiągnęłyśmy, also keeping the ę. The ą only remains in the masculine singular, like osiągnął (he reached).

Why is the mountain (góra) written as góry here? Is it plural?